Question

Mohan takes 6 days less than ritu to finish a piece of work. If both of them together can finish the work in 4 days, in how many days will ritu alone can finish the work ​

Answer 1

Answer:

2 days because Mohan takes 6 days when Ritu is doing only 2 days.

Answer 2

Ritu alone can finish the piece of work in 12 days.

• Let the total work be taken as 1.

• Let the number of days taken by Ritu to finish a piece of work alone be x.

=> Number of days taken by Mohan to finish the work alone = x - 6

• Work done by Ritu in one day = 1 / x

Work done by Mohan in one day = 1 / (x - 6)

∴  Work done by Ritu and Mohan together in one day = (1 / x) + {1 / (x - 6)}

• Given,

Number of days taken by Ritu and Mohan to complete the work together = 4

=> Work by them together in one day = 1 / 4

• According to the question,

(1 / x) + {1 / (x - 6)} = 1 / 4

Or, { (x - 6) + x } / x(x - 6) = 1 / 4

Or, x - 6 + x / x² - 6x = 1 / 4

Or, 2x - 6 / x² - 6x = 1 / 4

Or, 4 (2x - 6) = x² - 6x

Or, 8x - 24 = x² - 6x

Or, x² - 6x - 8x + 24 = 0

Or, x² - 14x + 24 = 0   [Quadratic equation]

• x² - 14x + 24 = 0  

Or, x² - 12x - 2x + 24 = 0

Or, x ( x - 12) - 2 ( x - 12 ) = 0

Or, ( x - 12 ) ( x - 2 ) = 0

Or, x - 12 = 0 ; x - 2 = 0

Or, x = 12  ;  x = 2

• The number of days cannot be 2 since Ritu and Mohan together complete the work in 4 days.

Therefore,  Ritu must require more than 4 days to complete the work alone.

• So, 2 gets discarded and 12 is the number of days in which Ritu can finish the work alone.